Some good advice already listed - I thought I'd also throw in some additional advice/suggestion for those taking such shots.
I often photograph birds and other wildlife in my backyard, which is hemmed in by a hedge and wall to the rear, and fences left and right - not the most natural looking environment. One method I often take is to not actually photograph the birds at the feeder, but stake out a nearby tree or bush where the birds are gathering waiting their turn at the feeder. I also track them back from the feeder to whatever tree or bush they fly to - and that's where I try to concentrate my photography. Works pretty well in mostly avoiding any clues that I'm in a backyard. Of course, you must have some nearby tree or bush that is accessible - if your backyard is devoid of any other plant life or tree, then you need to try something artificial, or might be out of luck.
Another method though is to just take photos of the bird with manmade objects in the shot. It much depends on how I want to use the photos - if they are more 'nature' shots where I want to share them with other birders and have it look more natural, I'll strive to avoid manmade objects. But sometimes it's also fun to capture some shots that specifically show it was done in my backyard - because sometimes it's fun to share what we find in our yards. Especially with my odd Florida diversity, I like to show pics of snakes, iguanas, lizards, passerines, waders, ducks, raccoons, squirrels, and opossum - and 'prove' that all those things were captured in the backyard. Having a lamppost, feeder, pool tiles, manicured lawn, or fence in the shot places the subject verifiably in my yard.
Here are my 'at home' galleries, divided up to blue jays, squirrels, other birds, lizards, and yard in general:
http://www.pbase.com/zackiedawg/at_home_with_the_h5
You'll see i've got some shots that don't show the 'yard' in the shot, while others embrace it.